Geometry Curriculum MAP OFFICIAL
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ABCDE
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Geometry Curriculum Unit
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Name of Course:Geometry Grade Level(s):9, 10, 11, 12
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Brief Description (Course Catalog):Geometry:
This course is a comprehensive study of plane and solid geometry including constructions, formulas for
measurement, and formal proofs. It is based on axioms and theorems that relate to points, lines, planes, and
solids. Algebraic techniques are integrated into the solution of many geometric problems.
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Length of Course (Qtr, Sem or Year):This is a one year course.
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Instructional Unit #1
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Name of Unit/Big Idea:Unit #1 Introduction to Geometry (Chapter 1)
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Brief Description:Students will review definitions of points, lines, distance between two points, midpoint, endpoint, components of parallel and perpendicular lines the distance formula.
Students will learn how to: Identify and define a plane, collinear and coplanar points, segment, vertex, angle, interior and exterior angles, adjacent, vertical, complementary and supplementary, linear pairs, angle measures (including notation), bisector, and define congruence and notation.
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Length of Unit (Days/Weeks):14
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Essential Questions:What is the language of Geometry?
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Content Standards:CRS: 1315.J, 2832.T,
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Common Core State ELA or Math Standards:CCSS: G-CO.1, G-GPE.6, 4.MD.C.7
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Power Standards: SWBAT:
1. Use correct notation and apply the definitions of introductory geometry.
2. Apply betweenness, midpoint, and distance formulas to find missing values.
3. Identify angle pairs and apply their properties.
4. Create introductory constructions.
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Students will need to know . . . (vocabulary & skills)Students will be able to . . . (performance)Resources and assessments
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1. Review definition of naming points, lines and planes (G.CO.1) 2. Identify segment measures, midpoint of segment and determine midpoint on coordinate plane (G-GPE.6) 3. Find the union and intersection of points lines, line segment, rays, and angles (G.CO.1) 4. Find missing measures of segment or angles by using system of equations or quadratic equations 5. Vocabulary: collinear, coplanar, betweeness, and congruenceLevel 1
1. Identify and name points, lines, and planes
2. Identify collinear and coplanar points
3. Identify the intersection of lines
4. Apply betweenness of points to determine line segment lengths using real numbers and algebra.
5. Determine if two line segments are congruent.
6. Find the distance between two points on a number line
7. Find the midpoint of a line segment on a number line.
8. Find the midpoints of a line segment on a co-ordinate plane.
9. Given a point is the midpoint, find the length of each segment given numerical lengths .
10. Given a point is the midpoint, find the length of each segment using algebra
11. Classify angles
12. Define all the components of an angle: vertex, sides (rays), interior and exterior
13. Given that a ray is an angle bisector, find the measure of each angle with and without algebra
14. Identify and name pairs of angles: adjacent, vertical, complementary, supplementary, linear pairs,
15. Find the complement and supplements to angles with given measures.
16. Determine if two lines are perpendicular given the measures of the angles they form.
Level 2

17. Construct congruent segments, congruent angles, perpendicular bisector, and angle bisectors.
18. Find the coordinates of an endpoint of a line segment given its midpoint and the other endpoint.
19. Find the measures of two supplementary or complementary angles given information in word problem format about the two angles.
20. Find missing segment or angle measures by solving factorable quadratic equations with a leading coefficient of 1.
Level
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21. Find the union and intersection of points, lines, lines segments, rays and angles.
22. Find the missing co-ordinate of an endpoint of a line segment given its length.
23. Find missing segment or angle measures by employing systems of equations.
24. Find missing segment or angle measures by solving quadratic equations.

CSL Quiz (Spiral Review)
Common Assessments:
Unit #1Test
Daily Assessment:
Formative assessments will
be given independently by
teachers.

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Instructional Unit #2
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Name of Unit/Big Idea:Unit #2 Reasoning and Proof (Chapter 2)
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Brief Description:Students will learn how to: Make conjectures and find out if they are true/false based on given information; Create a hypothesis, conclusion of a conditional statement; Apply the following properties to real numbers using Algebra Proofs: reflexive, symmetric, transitive, addition, subtraction, multiplication, division, substitution and distributive.
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Length of Unit (Days/Weeks):13 Days
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Essential Questions:How can one use reasoning and logic to make a mathematical argument?
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Content Standards:CRS: 1315.I, 1315.J, 2427.Y
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Common Core State ELA or Math Standards:CCSS: G-CO.C.9
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Reporting Targets:SWBAT:
1. Reason with basic geometric definitions, postulates, and theorems.
2. Write two column proofs.
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Students will need to know . . . (vocabulary & skills)Students will be able to . . . (performance)Resources and assessments
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1. The following properties for Algebra Proofs: reflexive, symmetric, transitive, addition, subtraction, multiplication, division, substitution and distributive.
2. Write and create a hypothesis, conjecture from true/false logic statements
3. Segment and angle addition, subtraction
4. Bisector and Midpoint
Level 1
1. Draw a conlcusion based (construct viable arguments) on given information, pimarily midpoint, bisect, or perpendicular.
2. If a conjecture is false, provide a counterexample.
3. Write a conditional statement in “if-then” form.
5. Identify the hypothesis and conclusion of a conditional statement.
6. Prove angles congruent if they are vertical or right angles.
7. Apply postulates regarding points, lines and planes and their intersections.
8. Apply the following properties of real numbers: Reflexive, Symmetric, Transitive, Addition, Subtraction, Multiplication, Division, Substitution, Distributive Properties.
9. Write a two column algebraic Proof
10. Apply the definition of complementary and supplementary to find the measure of an angle or unknown.
Level
2
12. Solve for the measure of two supplementary/complementary angles given their ratio.
13. Critique a statement using a counterexample to a false statement.
Lev
el 3
14. Find the inverse, converse and contrapositive of a conditional statement.
15. Apply the properties of addition, subtraction, multiplication and division to geometric proofs.
16. Apply the contrapositive to draw conclusion given a series of true conditional statements.
17. Apply the definition of complementary and supplementary to write proofs.

CSL Quiz (Spiral Review)
Common Assessments:
Unit #2Test
Daily Assessment:
Formative assessments will
be given independently by
teachers.
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Instructional Unit #3
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Name of Unit/Big Idea:Unit #3 Parallel and Perpendicular Lines and Parallelogram (Chapter 3)
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Brief Description:Students will learn to: Determine if lines are parallel or perpendicular by finding slope of the two lines; Name pairs of angles of two parallel lines and a transversal ; Use properties of parallel lines to determine relationship between angles as congruent angle or supplementary angles in a parallelogram; use logic to write a proof about parallel lines and a transversal properties; Be able to construct parallel and perpendicular lines.
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Length of Unit (Days/Weeks):Approximately 13-15 days
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Essential Questions:Can one create, find, and manipulate parallel and perpendicular lines?
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Content Standards:CRS: 1619.N, 2023.N, 2023.P, 2427.Z, 3336.P
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Common Core State ELA or Math Standards:CCSS: A-CED.1,G-CO.9, G-GPE.5,GPE.1
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Reporting Targets:SWBAT:
1. Identify angle pairs and apply their properties when two parallel lines are crossed by a transversal.
2. Write the equations for parallel and perpendicular lines.
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Students will need to know . . . (vocabulary & skills)Students will be able to . . . (performance)Resources and assessments
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1. How to write the equation of a line in slope-intercept form
2. Definitions of Congruent and supplementary angles
3. How to write an equation for two congruent or supplementary angles.

Level 1

1. Identify whether a pair of lines is parallel, perpendicular or skew.
2. Name the pairs of angles formed by two lines and a transversal.
3. Use the properties of parallel lines to determine congruent angles.
4. Use the properties of parallel lines to determine supplementary angles.
5. Find the slope of a line given two points.
6. Determine whether two lines are parallel or perpendicular based on their slopes.
7. Write the equation of a line in slope-intercept form given the slope and y-intercept.
8. Write the equation of a line in slope-intercept form given the slope and a point on the line.
9. Write the equation of a line in slope-intercept form given the graph of the line.
10. Write the equation of a line in slope-intercept form given the graph of a line parallel or perpendicular to the line and another point on the line.
11. Apply the angle sum theorem.

Level 2

12. Write geometric proofs involving parallel lines cut by a transversal.
13. Find for what angle measures (or values of x) two lines are parallel.
14. When two lines are cut by a transversal and congruent or supplementary angles, conclude that lines are parallel.

Level
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15. Given the slope and two points on the line, one of which is missing a coordinate, find the missing coordinate.
16. Find the perpendicular bisector of a segment.
17. Given parallel lines cut by a transversal, write two column proofs to prove congruent or supplementary angle pairs.
18. Given two lines cut by a transversal and congruent or supplementary angles, write two column proofs to prove lines parallel.

CSL Quiz (Spiral Review)
Common Assessments:
Unit #4Test
Daily Assessment:
Formative assessments
will be given
independently by
teachers.
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Instruction Unit #4
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Name of Unit/Big Idea:Congruent Triangles (Chapter 4)
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Brief Description:Students will be able to prove if two triangles are congruent and show that corresponding sides and angles are proportional/congruent.
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Length of Unit (Days/Weeks):15 Days
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Essential Questions:What must be true for two triangles to be congruent?
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Content Standards:G403; G503; G603
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Common Core State ELA or Math Standards:G-SRT.B.5; G-CO.D. 12;
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Reporting Targets:SWBAT:
1. Classify triangles and apply their properties.
2. Prove triangles congruent.
3. Apply Angle Sum Theorem
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Students will need to know . . . (vocabulary & skills)Students will be able to . . . (performance)Resources and assessments
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How to classify triangles based on angles and sides.Level 1
1. Apply properties of isosceles triangles.
2. Apply properties of equilateral triangles.
3. Apply the Angle Sum Theorem to find missing angle values.
4. Determine congruent relationships between corresponding sides and angles of congruent triangles.
5. Prove triangles are congruent by applying the following postulates: SSS, SAS, AAS, ASA
6. Apply the angle-sides theorem of isosceles triangles.
7. Apply the equilateral-equiangular corollary.
Level 2
8. Prove triangles congruent by HL
9. Prove overlapping triangles congruent.
10. Verify triangle congruence given the coordinates of the vertices.
Level
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11. Use the definitions of altitudes, medians, and angle bisectors in triangle congruence proofs.
12. Apply the Pythagorean Theorem corollary to classify triangles by angles given the coordinates of the vertices.
Quizzes
Exams
CSLQuizzes (Spiral throughout the year)
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Instructional Unit #5STATS
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Name of Unit/Big Idea:Relationships Within Triangles (Chapter 5)
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Brief Description:Students will learn how to:
Apply definition of Median by finding missing segment lengths and find endpoints of the median using the midpoint formula; Determine the median point of a line segment on a coordinate plane; Use the definition of median in a two-column direct proof; Given a set of angles, use the Exterior Angle Theorem to determine the missing angle measure; Use the Triangle Inequality Theorem to determine whether the three sides create a triangle; Apply the Sum of Interior Angles of a Triangle Theorem; Identify and classify triangles by the angles and sides; Identify and write the equation of a line containing the median, altitude and perpendicular bisector of a triangle(
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Length of Unit (Days/Weeks):10 Days
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Essential Questions:What is the relationship between special segments in triangles?
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Content Standards:CRS: 1315.B, 1619.A, 1619.K. 2023.A, 2023.S, 2427.W, 2427.Y, 2832.A, 3336.A
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Common Core State ELA or Math Standards:CCSS: G-CO.D.12,G.CO.C.10, G-SRT.B.5
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Reporting Standards:SWBAT:
1. Apply properties of special segments in triangles to determine missing angles and segment lengths.
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Students will need to know . . . (vocabulary & skills)Students will be able to . . . (performance)Resources and assessments
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1. Use the midpoint formula on a coordinate plane
2. Find missing side lengths of a triangle given the midpoint and one endpoint
3. Classifications of triangles by side and angles
4. Algebraically find the measure of an angle given it is theangle bisector of angle in a triangle
Level I
1. Apply definition of Median by finding missing segment lengths and find endpoints of the median using the midpoint formula
2. Determine the median point of a line segment on a coordinate plane
4. Given a set of angles, use the Exterior Angle Theorem to determine the missing angle measure
5. Use the Triangle Inequality Theorem to determine whether the three sides create a triangle
6. Apply the Sum of Interior Angles of a Triangle Theorem
7. Find the length of the midsegment
8. Apply the Perpendicular Bisector Theorem.
Level 2

7. Use the definition of median, altitude, perpendicular, angle bisector in a two-column direct proof.
CSL Quiz (Spiral Review)
Common Assessments:
Unit #5 Test
Daily Assessment:
Formative assessments
will be given
independently by
teachers.
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Instructional Unit # 6STATS UNIT
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Name of Unit/Big Idea:Proporties of Quadrilaterals (Ch. 6)
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Brief Description:Students will explore relationships in quadrilaterals, classifying them on certain criteria, and applying the properties to find different side lengths and angle measures.
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Length of Unit (Days/Weeks):12 Days
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Essential Questions:Under what conditions are certain quadrilaterals are formed?
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Content Standards:G405; G505
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Common Core State ELA or Math Standards:G-CO.C.11; G-SRT.B.5,
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Reporting Standards:SWBAT:
2. Find interior and exterior angles of convex polygons.
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Students will need to know . . . (vocabulary & skills)Students will be able to . . . (performance)Resources and assessments
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Enter what the students need to know such as vocabulary and skills in order to achieve the performance levelEnter what students will be able to do. At the end of each statement, the content/CCSS standard should be listed with itAny item that is a common assessment or common resources needs to be listed here.
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Level 1

1. Find the sum of the interior angles of a convex polygon.
2. Use the measure of one exterior angle of a convex polygon.
3. Find the measure of one interior angle of a convex polygon.
4. Apply the properties of a parallelogram.
5. Prove that a quadrilateral is a parallelogram.
6. Apply the properites of a rhombus, rectangles and squares.
7. Argue that a quadrilateral is a rhombus, rectangle or square. .
8. Apply the properties of a trapezoid.

Level 2

9. Given the coordinates of a quadrilateral, determine the most specific name for the quadrilateral.

Level 3

10. Use two column proofs to prove a quadrilateral is a parallelogram, rhombus, rectangle, square, kite, and trapezoid
Quizzes and tests
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Instructional Unit #7
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Name of Unit/Big Idea: Similarity (Chapter 7)
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Brief Description:Students will learn how to:
Name and label corresponding parts of similar polygons and triangles; Find a missing side or angle given similar polygons or triangle using similarity; Study Right, Isosceles, Acute and Obtuse Triangles similarity and/or congruence; Prove that two triangles are congruent using Angle-Side-Angle, Angle-Angle-Side, Side-Side-Side and Side-Angle-Side postulates for triangle congruence; Write a formal two-column proof that lists the logical path
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Length of Unit (Days/Weeks):13 days
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Essential Questions:What relationships/proportions exist in similar figures?
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Content Standards:CRS: 2023.P, 2023.S, 2427.BB, 2832.W, 2832.X2832.AA, 3336.A, 3336.Q
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Common Core State ELA or Math Standards:CCSS: G.SRT.2, G.SRT.B.4; G.SRT.B.5
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Reporting Standards:SWBAT:
1. Use properties of similar figures to find missing angles, side lengths, and scale factors.
2. Prove triangles similar.
3. Use proportional relationships in geometric figures.
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Students will need to know . . . (vocabulary & skills)
Resources and assessments
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uLevel 1

1. Solve a proportion involving linear equations
2. Write a proportion and solve from a word problem
3. Identify similar figures
4. Write a similarity statement given measures of sides and/or angles of two similar figures
5. Determine the scale factor between two similar figures
6. Find a missing side length between two similar figures
7. Prove two triangles similar
8. Use the Side-Splitter Theorem to find missing segment lengths
9. Use the Angle Bisector Theorem to find missing segment lengths

Level 2

10. Solve a proportion involving quadratic equations
11. Find missing side lengths of two overlapping similar triangles
12. Use proportions to find a missing perimeter of two similar triangles/figures

Level 3

13. Prove corresponding sides of similar triangles are proportional
14. Use means/extremes product theorem in proofs
CSL Quiz (Spiral Review)
Common Assessments:
Unit #6 Test
Daily Assessment:
Formative assessments
will be given
independently by
teachers.
Projects: ?
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Instruction Unit #8
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Name of Unit/Big Idea:
Right Triangles and Trigonometry (Chapter 8)
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Brief Description:Students will be able to solve right triangles
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Length of Unit (Days/Weeks):25 Days
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Essential Questions:Can you solve a right triangle?
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Content Standards:
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Common Core State ELA or Math Standards:G-SRT.C.8, G-SRT.B.4, G-SRT.C.8, G-SRT.C.7, G-MG.A.1, G-SRT.D.10
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Reporting Targets:
SWBAT:
1. Use Pythagorean Theorem to find missing side lengths and angle measures.
2. Apply right triangle trigonometry to find missing side lengths and angle measures.
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Students will need to know . . . (vocabulary & skills)Students will be able to . . . (performance)Resources and assessments
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how to solve right triangles given different information.
Level 1
1. Determine if three values could be the measures of a right triangle by applying the Pythagorean Theorem.
2. Find the missing side length of a right triangles given two sides.
3. Find two missing side lengths of a 30-60-90 triangle given one side
4. Find two missing side lengths of a 45-45-90 triangle given one side
5. Write the trig ratio for any angle in a right triangle
6. Use a calculator to determine the given trig value for angle
7. Use trig to find a missing side length
8. Use trig to find a missing angle measure

Level 2
9. Apply 30-60-90 and 45-45-90 triangles to word problems involving diagonals of squares and altitudes of equilateral triangles
10. Apply the Angle of Elevation/Angle of Depression to find missing angles/side lengths

Level 3
11. Use the definitions of altitudes, medians, and angle bisectors in triangle congruence proofs.
12. Apply the Pythagorean Theorem corollary to classify triangles by angles given the coordinates of the vertices.
13. Apply the Altitude on Hypotenuse Theorems to find missing segment lengths.
14. Use trig to find missing side/angle measures in a 3D figure.
15. Apply law of sines to find missing side lengths and angles
16. Apply law of cosines to find missing side lengths and angles
Quizzes
Exams
CSLQuizzes (Spiral throughout the year)